pub fn new_birthday_probability(n: u32) -> f64 {
    // P = 1 - P_{nooverlay} = 1 - \prod_{i = days - n + 1}^days {i / 365}
    let mut pro_no_overlay = 1.0;
    const DAYS:u32 = 365;
    for i in (DAYS - n + 1)..=DAYS {
        pro_no_overlay *= i as f64 / DAYS as f64;
    }
    1.0 - pro_no_overlay
}
